In [10] we considered a class of hyperbolic endomorphisms and asked the question whether there exists a physically motivated invariant measure (SRB measure) and if so we gave a criterion when the map is invertible on a set of full measure. In this work we want to consider a particular example of this class — in fact a three-parameter family of those — and prove that a.s. the criterion is fulfilled. From this it follows that the Young formulae for the Hausdorff dimension of the SRB measure holds.